Now, diving right into the twisty and exciting world of Boruto! To answer your question, Boruto Uzumaki, as of the latest episodes, doesn't possess the Byakugan per se, but he does have a unique eye ability known as the Jougan.
The Byakugan, primarily utilized by the Hyuga clan, is one of the 'Three Great Dojutsu', alongside with the Sharingan and Rinnegan. Known for its nearly 360-degree vision, it's a truly formidable ability in the ninja world. Boruto, being the son of Hinata Hyuga, naturally draws some speculations about whether he will awaken the Byakugan.
However, what we see in Boruto's eye is not the classic Byakugan but something new and unique, referred to as the Jougan. Its name literally means 'Pure Eye' and it's been shown to have several powerful abilities, like being capable of seeing the flow of chakra, the hidden dimensions or predict someone's movement. Moreover, Boruto's Jougan seems to have a close connection with the ongoing plot of the Otutsuki Clan.
The whole 'Will Boruto get a Byakugan?' speculation might get more twist as the anime series progress. Because, in the story, it was also hinted that Boruto might have some more latent abilities due to his unique lineage and exposure to various powers (such as Naruto's Uzumaki and Hyuga heritage plus his direct contact with an Otutsuki).
So far, the anime has been pretty hush-hush about the full extent of Boruto's Jougan ability and how it'll progress. So, while we can't say for sure about'Boruto having Byakugan', the Jougan in itself is an exciting and powerful new addition to the Naruto universe. So, stay tuned to unearth more of Boruto's mysterious power!